zerodha.com/varsity 49
1. The density curve is calculated based on the time series data, and the time series
data in our context is the ‘ratio’ – as you may recall from the previous chapter, the
main inputs to calculate the density curve is the ratio’s time series, the ratio’s
mean, and the ratio’s standard deviation
2. The density curve is a value – varying between 1 and 0. The value of the density
curve helps us understand the probability of the ratio, falling back to the mean.
I understand the 2
nd
statement may confuse some of the readers, but at this point, I’d
suggest you keep this statement in mind. You will understand what I mean by this as we
proceed.
Let us spend a little time on the normal distribution, I know we have discussed this
multiple times in the past, but bear with me one more time.
The time series data (like the ratio) typically have an average (or mean) value. For
example, the average value for the ratio time series is 1.87 (we calculated this in the earlier
chapter). More often than not, the value of the ratio tends to lie around the mean value. If
the value of the ratio drifts away from the mean, then one can expect the value of the ratio
to gravitate back to the mean.
For example, if the latest value of the ratio shoots up to 2.5, then over time, one can
expect the value of the ratio to fall to 1.87 and likewise if the value of the ratio plummets.
Now here is a question – If the ratio drifts away from the mean (which is bound to happen
on a daily basis), is there a way wherein we can quantify the probability of the ratio to
move back to the mean, again?
For example, if the latest ratio value is at 2.5, we all know it will fall to a mean of 1.87, but
what is the probability of this occurring? Is it 10%, 20% or 90%?
This is where the density curve comes in handy. The value of the density curve tells us how
far, in terms of standard deviation, the ratio has deviated away from its mean. Now, if the
value is in terms of standard deviation, then naturally there is a probability assigned to it,
and eventually, this probability helps us set up a trade.